Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Textbook Question
Chapter 20, Problem 16A
Express each value as a percent.
16. 1.33
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a) Suppose that we are carrying out the 1-phase simplex algorithm on a linear program in
standard inequality form (with 3 variables and 4 constraints) and suppose that we have
reached a point where we have obtained the following tableau. Apply one more pivot
operation, indicating the highlighted row and column and the row operations you carry
out. What can you conclude from your updated tableau?
x1 12 23
81
82
83
S4
$1
-20
1 1
0
0
0
3
82
3 0
-2
0
1
2
0
6
12
1
1
-3
0
0
1
0
2
84
-3 0
2
0
0
-1 1 4
2
-2
0 11
0
0
-4
0
-8
b) Solve the following linear program using the 2-phase simplex algorithm. You should give
the initial tableau and each further tableau produced during the execution of the
algorithm. If the program has an optimal solution, give this solution and state its
objective value. If it does not have an optimal solution, say why.
maximize 21 - - 2x2 + x3 - 4x4
subject to 2x1+x22x3x4≥ 1,
5x1+x2-x3-4 -1,
2x1+x2-x3-342,
1, 2, 3, 4 ≥0.
Suppose we have a linear program in standard equation form
maximize c'x
subject to Ax=b,
x≥ 0.
and suppose u, v, and w are all optimal solutions to this linear program.
(a) Prove that zu+v+w is an optimal solution.
(b) If you try to adapt your proof from part (a) to prove that that u+v+w
is an optimal solution, say exactly which part(s) of the proof go wrong.
(c) If you try to adapt your proof from part (a) to prove that u+v-w is an
optimal solution, say exactly which part(s) of the proof go wrong.
(a) For the following linear programme, sketch the feasible region and the direction
of the objective function. Use you sketch to find an optimal solution to the
program. State the optimal solution and give the objective value for this
solution.
maximize +22
subject to 1 + 2x2 ≤ 4,
1 +3x2 ≤ 12,
x1, x2 ≥0
(b) For the following linear programme, sketch the feasible region and the direction
of the objective function. Explain, making reference to your sketch, why this
linear programme is unbounded.
maximize
₁+%2
subject to
-2x1 + x2 ≤ 4,
x1 - 2x2 ≤4,
x1 + x2 ≥ 7,
x1,x20
Give any feasible solution to the linear programme for which the objective
value is 40 (you do not need to justify your answer).
Chapter 20 Solutions
Mathematics for Machine Technology
Ch. 20 - Prob. 1ACh. 20 - Prob. 2ACh. 20 - Prob. 3ACh. 20 - Prob. 4ACh. 20 - Prob. 5ACh. 20 - Compute (15314)18+734 . Express the answer as a...Ch. 20 - Prob. 7ACh. 20 - Prob. 8ACh. 20 - Prob. 9ACh. 20 - Prob. 10A
Ch. 20 - Prob. 11ACh. 20 - Prob. 12ACh. 20 - Prob. 13ACh. 20 - Express each value as a percent. 14. 0.062Ch. 20 - Prob. 15ACh. 20 - Express each value as a percent. 16. 1.33Ch. 20 - Prob. 17ACh. 20 - Prob. 18ACh. 20 - Prob. 19ACh. 20 - Prob. 20ACh. 20 - Prob. 21ACh. 20 - Prob. 22ACh. 20 - Prob. 23ACh. 20 - Prob. 24ACh. 20 - Prob. 25ACh. 20 - Prob. 26ACh. 20 - Prob. 27ACh. 20 - Prob. 28ACh. 20 - Prob. 29ACh. 20 - Prob. 30ACh. 20 - Prob. 31ACh. 20 - Prob. 32ACh. 20 - Prob. 33ACh. 20 - Prob. 34ACh. 20 - Prob. 35ACh. 20 - Prob. 36ACh. 20 - Prob. 37ACh. 20 - Prob. 38ACh. 20 - Prob. 39ACh. 20 - Prob. 40ACh. 20 - Prob. 41ACh. 20 - Prob. 42ACh. 20 - Prob. 43ACh. 20 - Prob. 44ACh. 20 - Prob. 45ACh. 20 - Prob. 46ACh. 20 - Prob. 47ACh. 20 - Prob. 48ACh. 20 - Prob. 49ACh. 20 - Express each percent as a common fraction or mixed...Ch. 20 - Prob. 51ACh. 20 - Prob. 52ACh. 20 - Prob. 53ACh. 20 - Prob. 54ACh. 20 - Prob. 55ACh. 20 - Prob. 56ACh. 20 - Prob. 57ACh. 20 - Prob. 58A
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